Louder, L;
Wilton, H;
(2024)
Uniform negative immersions and the coherence of one-relator groups.
Inventiones Mathematicae
10.1007/s00222-024-01246-4.
(In press).
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Abstract
Previously, the authors proved that the presentation complex of a one-relator group G satisfies a geometric condition called negative immersions if every two-generator, one-relator subgroup of G is free. Here, we prove that one-relator groups with negative immersions are coherent, answering a question of Baumslag in this case. Other strong constraints on the finitely generated subgroups also follow such as, for example, the co-Hopf property. The main new theorem strengthens negative immersions to uniform negative immersions, using a rationality theorem proved with linear-programming techniques.
| Type: | Article |
|---|---|
| Title: | Uniform negative immersions and the coherence of one-relator groups |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00222-024-01246-4 |
| Publisher version: | http://dx.doi.org/10.1007/s00222-024-01246-4 |
| Language: | English |
| Additional information: | Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10188998 |
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